Question

Determine the nuclear radius (in fm) for each of the following nuclei.

a) 126C
b) 147N
c) 6027Co
d) 20882Pb

Answer 1

(a) 2.75 fm

(b) 2.89 fm

(c) 4.70 fm

(d) 7.12 fm

Step-by-step explanation:

For a given element, the radius r of its nuclei is given by;

r = r₀
`A^((1/3))`

Where;

A = Atomic mass of the element

r₀ = 1.2 x 10⁻¹⁵m = 1.2fm

Now let's solve for the given elements

(a) ¹²₆C

Carbon element => This has an atomic mass number of 12

Therefore its radius is given by;

r = 1.2 x
`12^(1/3)`

r = 1.2 x 2.29

r = 2.75 fm

(b) ¹⁴₇N

Nitrogen element => This has an atomic mass number of 14

Therefore its radius is given by;

r = 1.2 x
`14^(1/3)`

r = 1.2 x 2.41

r = 2.89 fm

(c) ⁶⁰₂₇Co

Cobalt element => This has an atomic mass number of 60

Therefore its radius is given by;

r = 1.2 x
`60^(1/3)`

r = 1.2 x 3.92

r = 4.70 fm

(d) ²⁰⁸₈₂Pb

Lead element => This has an atomic mass number of 208

Therefore its radius is given by;

r = 1.2 x
`208^(1/3)`

r = 1.2 x 5.93

r = 7.12 fm